1. Field of the Invention
The present invention relates generally to a multi-input multi-output-orthogonal frequency division multiplexing (MIMO-OFDM) communication system, and in particular, to a method and apparatus for transmitting a preamble for frame synchronization.
2. Description of the Related Art
OFDM is widely considered an essential transmission scheme for next-generation wireless communications for its simple implementation, robustness against multi-channel fading, and its capability of increasing the data rate through parallel transmission of data signals at frequencies called sub-carriers. The sub-carriers are mutually orthogonal to avoid inter-carrier interference. Their spectrums are overlapped so that the sub-carriers are spaced from each other with a minimum gap.
An OFDM system is sensitive to errors or offsets including a frequency offset, timing errors in a frame or a symbol, and non-linearity caused by a high peak-to-average power ratio (PAPR). Some OFDM systems utilize a coherent detection rather than differential modulation and demodulation in order to achieve an additional signal-to-noise ratio (SNR) gain of about 3 dB. Their performance depends considerably on whether or not channel state information (CSI) is available.
The use of multiple transmit/receive antennas further improves communication quality and throughput in an OFDM system. This OFDM system is called a MIMO-OFDM system which is distinguished from a single-input single-output (SISO)-OFDM system.
The MIMO-OFDM system can simultaneously transmit data on a plurality of sub-channels in the space domain irrespective of whether or not a transmitter requires the CSI. The sub-channels refer to radio paths from a plurality of transmit antennas to a plurality of receive antennas. Thus, the MIMO-OFDM system offers a higher data rate than the SISO-OFDM system.
Typically, the MIMO/SISO-OFDM system requires frame synchronization in both time and frequency and estimation of channel parameters and noise changes. For the synchronization and estimation, a preamble sequence (i.e. training symbols or a training sequence) is used.
FIG. 1 illustrates the structure of an OFDM frame including a preamble sequence in a typical OFDM communication system. Referring to FIG. 1, the preamble sequence consists of special symbols added as a prefix to the OFDM frame. In general, the structure and contents of the preamble are known between a transmitter and a receiver. The preamble is so configured as to have a relatively low complexity and offer a maximum performance in the synchronization and estimation process.
An ideal preamble configuration satisfies the following requirements:
(1) Excellent compensation for timing synchronization;
(2) Low PAPR for high-power transmission;
(3) Feasibility for channel estimation;
(4) Feasibility for frequency offset estimation over a wide range; and
(5) Low computation complexity, low overhead and high accuracy.
A description will be made below of conventional preamble structures for MIMO-OFDM frame synchronization and channel estimation.
A first known preamble transmitting/receiving scheme for MIMO-OFDM frame synchronization transmits the same information sequence through all transmit antennas.
The MIMO-OFDM system must have excellent properties in time-domain periodic auto-correlation of sequences as well as in cross-correlation of sequences transmitted from different transmit antennas. Ideal auto-correlation and cross-correlation properties are determined by Equation (1) and Equation (2), respectively:
                              ϕ          ⁡                      (            k            )                          =                                            ∑                              n                =                0                                            N                -                1                                      ⁢                                          s                                  q                  ,                  n                                *                            ·                              s                                  q                  ,                                                            (                                              n                        +                        k                                            )                                        N                                                                                =                      {                                                            1                                                                      k                    =                    0                                                                                                0                                                                      k                    ≠                    0                                                                                                          (        1        )                                                      Ψ            ⁡                          (              k              )                                =                                                    ∑                                  n                  =                  0                                                  N                  -                  1                                            ⁢                                                s                                      q                    ,                    n                                    *                                ·                                  s                                                            q                      ′                                        ,                                                                  (                                                  n                          +                          k                                                )                                            N                                                                                            =                          0              ⁢                                                          ⁢              for              ⁢                                                          ⁢              all              ⁢                                                          ⁢              k                                      ,                  q          ≠                      q            ′                                              (        2        )            where superscript * denotes a conjugate operator, N denotes the length of sequences, q and q′ denote indexes of transmit antennas, and sq,n denotes an nth data symbol in a sequence of length N transmitted from a qth transmit antenna. A sequence that satisfies Equation (1) is an orthogonal sequence. Here, subscript N denotes the period of the sequence.
In an ideal situation a space-time matrix for sequences transmitted from N transmit antennas is a unit matrix. However, this is impossible in its application because the number of the transmit antennas must be equal to the length of the sequences.
In the first preamble transmitting/receiving scheme, a preamble sequence is designed for frame synchronization by copying a predetermined orthogonal sequence designated for a first antenna to be used for the other antennas, and is represented bysq,n=sn for all q  (3)
A distinctive shortcoming of the above scheme is that SNR may be very low in the case of a correlated channel. For a 2×2 MIMO system using two transmit antennas and two receive antennas, for instance, a received signal is expressed as
                                          r            j                    ⁡                      [                          n              ,              k                        ]                          =                                            ∑              i                        ⁢                                                            H                  ij                                ⁡                                  [                                      n                    ,                    k                                    ]                                            ⁢                              S                ⁡                                  [                                      n                    ,                    k                                    ]                                                              +                                    n              j                        ⁡                          [                              n                ,                k                            ]                                                          (        4        )            where rj[n, k] denotes a frequency-domain signal received at a jth receive antenna, nj[n, k] denotes white Gaussian noise, Hij denotes a channel response from an ith transmit antenna to a jth receive antenna, and S [n, k] denotes an nth symbol in a k-th sub-carrier. As noted from Equation (4), if H1j is approximately equal to −H2j, the SNR of the received signal is very low.
Another conventional preamble transmitting/receiving scheme for MIMO-OFDM frame synchronization utilizes a direct modulated orthogonal poly-phase sequence.
A direct modulated orthogonal poly-phase sequence is a chirp-like sequence used to form a preamble sequence. If P is a prime number, the direct modulated orthogonal poly-phase sequence is comprised of (P−1) orthogonal sequences. Its excellent cross-correlation property is given as
                                          Φ            ⁡                          (              k              )                                =                                                    ∑                                  n                  =                  0                                                                      p                    2                                    -                  1                                            ⁢                                                s                                      q                    ,                    n                                    *                                ·                                  s                                                            q                      ′                                        ,                                                                  (                                                  n                          +                          k                                                )                                                                    p                        2                                                                                                                  ≤                                          1                                  p                  2                                            ⁢                                                          ⁢              for              ⁢                                                          ⁢              all              ⁢                                                          ⁢              k                                      ,                  q          ≠                      q            ′                                              (        5        )            
According to the second preamble transmitting/receiving scheme, the transmit antennas transmit the same preamble sequence having (P−1) orthogonal sequences. This scheme faces the following problems:
(1) Although the length of the direct modulated orthogonal poly-phase sequence is the square of a prime number, the length of an OFDM frame must generally be a power of 2, for example, 64, 128, 256, . . . ; and
(2) While an ideal frame must be acquired at each point, it is impossible to reduce the complex multiplications required and thus considerably greater computation is required.
Now, known preamble transmitting/receiving schemes for MIMO-OFDM channel estimation will be described below.
A first preamble transmitting/receiving scheme for MIMO-OFDM channel estimation is Geoffrey Li's single-symbol optimal training technique. FIG. 2 illustrates a preamble structure according to the first preamble transmitting/receiving scheme for MIMO-OFDM channel estimation.
Referring to FIG. 2, given Q transmit antennas, a first antenna transmits a preamble sequence S(t), and each of the other antenna transmits a preamble sequence S(t−T/Q), . . . , or S{t−(Q−1)T/Q} produced by rotating a preamble sequence for the previous antenna a predetermined number of symbols, that is, T/Q symbols. Q=Floor(N/L0) in which N is the number of sub-carriers and L0 is the maximum time delay spread of a sub-channel. Floor( ) is a function of obtaining an integer and T is the period of the preamble sequence. T is the product of the number of symbols included in the preamble sequence, N, and a symbol period Ts.
A received signal at the jth receive antenna is determined by
                                          r            j                    ⁡                      [                          n              ,              k                        ]                          =                                            ∑              i                        ⁢                                                            H                  ij                                ⁡                                  [                                      n                    ,                    k                                    ]                                            ⁢                              S                ⁡                                  [                                      n                    ,                    k                                    ]                                            ⁢                              W                N                                  k                  ·                                      L                    0                                                                                +                                    n              j                        ⁡                          [                              n                ,                k                            ]                                                          (        6        )            where WN represents an N-point fast Fourier transform (FFT). If p[n, k]=r[n, k]*S*[n, k], Equation (6) is expressed as
                                          P            j                    ⁡                      [                          n              ,              k                        ]                          =                                            ∑              i                        ⁢                                                            H                  ij                                ⁡                                  [                                      n                    ,                    k                                    ]                                            ⁢                              W                N                                                      -                    k                                    ·                                      L                    0                                                                                +                                                    n                j                            ⁡                              [                                  n                  ,                  k                                ]                                      ·                                          S                *                            ⁡                              [                                  n                  ,                  k                                ]                                                                        (        7        )            
FIG. 3 illustrates an example of the time-domain channel response characteristics of Pj[n, k]. Referring to FIG. 3, h0j is a channel response characteristic from a first transmit antenna to a receiver, h1j is a channel response characteristic from a second transmit antenna to the receiver, h2j is a channel response characteristic from a third transmit antenna to the receiver, and h3j is a channel response characteristic from a fourth transmit antenna to the receiver. Preamble sequences transmitted from the transmit antennas experience channels having different characteristics. The time-domain size T/Q of the channels varies with the number of the transmit antennas Q.
A mean square error (MSE) in the single-symbol optimal training technique is calculated by
                    MSE        =                                            L              0                        N                    ·                      σ            n            2                                              (        8        )            wherein, σn·−σn indicates a noise power.
In accordance with the first preamble transmitting/receiving scheme for MIMO-OFDM channel estimation, although a preamble sequence is transmitted on all sub-carriers, only one training sequence structure suffices. However, due to the rotation of a training sequence by a predetermined number of symbols for each transmit antenna, the number of transmit antennas is limited by the number of the rotated symbols and the length of the training sequence.
A second preamble transmitting/receiving scheme for MIMO-OFDM channel estimation utilizes Cordon L. Stuber and Apurva N. Mody's space-time coding. In this scheme, known symbols are orthogonally transmitted in the space domain through inversion and conjugation according to time and space, namely according to transmit antennas. A preamble sequence for a 2×2 system using two transmit antennas and two receive antennas is formed by
                    [                                                            S                1                                                                    S                2                                                                                        -                                  S                  2                  *                                                                                    S                1                *                                                    ]                            (        9        )            
The above matrix means that symbols S1 and S2 are sequentially transmitted from a first transmit antenna and symbols −S2* and S1* are sequentially transmitted from a second transmit antenna.
For a 4×4 system, a preamble sequence can be formed by
                    [                                                            S                1                                                                    S                1                                                                    S                1                                                                    S                1                                                                                        -                                  S                  2                                                                                    S                1                                                                    -                                  S                  4                                                                                    S                3                                                                                        -                                  S                  3                                                                                    S                4                                                                    S                1                                                                    -                                  S                  2                                                                                                        -                                  S                  4                                                                                    -                                  S                  3                                                                                    S                2                                                                    S                1                                                    ]                            (        10        )            
FIG. 4 illustrates transmission/reception of a preamble sequence according to the second preamble transmitting/receiving scheme for MIMO-OFDM channel estimation.
Referring to FIG. 4, Q preamble sequences, each having Q symbols are provided to Q transmit antennas from time t to time t+(Q−1)Ts through Q OFDM modulators. Ts is a symbol duration. The preamble sequences arrive at L receive antennas on Q×L sub-channels having channel response characteristics h11 to hQL. L OFDM demodulators collect signals R1 to RQL received at the L receive antennas from time t to time t+(T−1)Ts and form a Q×L received signal matrix.
In the second preamble transmitting/receiving scheme, the minimum number of training symbols needed for each transmit antenna is equal to the number of transmit antennas. As more training symbols are used, the preamble sequences are longer. This is not feasible for burst or high-mobility communications.